Daniel Jessie

Daniel Jessie is introducing a new mathematical approach to understanding the nature of dynamical network processes where standard mathematical tools can only provide analytical solutions in the simplest cases.

In the study of complex systems, a common approach is to use numerical techniques and simulations to analyze large-scale network models. However, these techniques do little to provide a general theoretical understanding of the nature of dynamical network processes. What is needed is a method of determining the behaviors of the system and understanding why they occur. However, standard tools are able to provide analytic solutions to only the simplest cases. The goal of this project is to introduce a different approach, and to work towards providing a more general understanding.

The mathematical techniques come mainly from abstract algebra, including representation theory and Lie groups, and have yet to be fully adapted to complex systems. Some initial work (e.g., [1]) has provided a method of finding generic behavior of dynamic network processes. Furthermore, the use of small-scale modeling becomes important. By providing tools to understand the behavior of smaller models, it then becomes possible to understand the issues that arise when the networks grow in size.

In previous work I applied these techniques to uniquely characterize the mathematical structure of strategic interaction, and this work is continuing to develop by incorporating a social structure to agents' behaviors. Furthermore, results on the mean-field approximation to dynamical network processes is providing insights into how network structures affect observable model behavior.